Liquid-liquid transition in ST2 water.

We use the weighted histogram analysis method [S. Kumar, D. Bouzida, R. H. Swendsen, P. A. Kollman, and J. M. Rosenberg, J. Comput. Chem. 13, 1011 (1992)] to calculate the free energy surface of the ST2 model of water as a function of density and bond-orientational order. We perform our calculations at deeply supercooled conditions (T = 228.6 K, P = 2.2 kbar; T = 235 K, P = 2.2 kbar) and focus our attention on the region of bond-orientational order that is relevant to disordered phases. We find a first-order transition between a low-density liquid (LDL, ρ ≈ 0.9 g/cc) and a high-density liquid (HDL, ρ ≈ 1.15 g/cc), confirming our earlier sampling of the free energy surface of this model as a function of density [Y. Liu, A. Z. Panagiotopoulos, and P. G. Debenedetti, J. Chem. Phys. 131, 104508 (2009)]. We demonstrate the disappearance of the LDL basin at high pressure and of the HDL basin at low pressure, in agreement with independent simulations of the system's equation of state. Consistency between directly computed and reweighted free energies, as well as between free energy surfaces computed using different thermodynamic starting conditions, confirms proper equilibrium sampling. Diffusion and structural relaxation calculations demonstrate that equilibration of the LDL phase, which exhibits slow dynamics, is attained in the course of the simulations. Repeated flipping between the LDL and HDL phases in the course of long molecular dynamics runs provides further evidence of a phase transition. We use the Ewald summation with vacuum boundary conditions to calculate long-ranged Coulombic interactions and show that conducting boundary conditions lead to unphysical behavior at low temperatures.